Real-time Snapshot Fractional Fourier Phase Retrieval via Deep Unfolding Network

Phase retrieval aims at recovering phase information from intensity observation patterns and realizing the reconstruction of images, which plays an important role in computational imaging. Recently, the near-field observation and reconstruction paradigm represented by fractional Fourier phase retrieval has broken through the limitations of traditional Fourier phase retrieval and realized single-shot phasing. However, existing reconstruction algorithms are mainly based on an optimized iterative framework that requires multiple iterations and relies on both accurate forward and backward projection, and thus cannot be applied to the fractional Fourier fast algorithm that lacks inverse transformations. So it limits the possibilities of real-time imaging to some extent. To address this challenge, this paper proposes a deep unfolding network, which introduces the fast fractional Fourier transform unfolded from an optimization iteration process. Through end-to-end training, the network can correct the error due to the inaccuracy of the inverse transform, achieving fast convergence and effective reconstruction. Experimental results show that the proposed method can utilize the fast fractional Fourier transform to achieve real-time snapshot phase retrieval.